English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this survey, we discuss some recent results on free boundary minimalsurfaces in the Euclidean unit-ball. The subject has been a very active fieldof research in the past few years due to the seminal work of Fraser and Schoenon the extremal Steklov eigenvalue problem. We review several differenttechniques of constructing examples of embedded free boundary minimal surfacesin the unit ball. Next, we discuss some uniqueness results for free boundaryminimal disks and the conjecture about the uniqueness of critical catenoid. Wealso discuss several Morse index estimates for free boundary minimal surfaces.Moreover, we describe estimates for the first Steklov eigenvalue on such freeboundary minimal surfaces and various smooth compactness results. Finally, wemention some sharp area bounds for free boundary minimal submanifolds andrelated questions.

Free boundary minimal surfaces in the unit ball : recent advances and open questions